1. Field of the Invention
This invention relates to an active filter having high Q value composed by the semiconductor integrated circuit.
2. Description of the Related Art
An example circuit of an active filter as a band stop filter (hereinafter, it is referred to as "TRAP") and an example circuit of an active filter for a band pass filter (hereinafter, it is referred to as "BPF"), which are generally used in conventional technology, are shown in FIG. 7 and FIG. 8 respectively. A transfer function H1 of the TRAP shown in FIG. 7 is described by Equation 1 if an inverse of a conductance gm.sub.1 of the first differential amplifier is represented as R.sub.1 and an inverse of a conductance gm.sub.2 of a second differential amplifier is represented as R.sub.2. A transfer function H2 of the BPF shown in FIG. 8 is described by Equation 2. EQU H1=(S.sup.2 +1/C.sub.1 C.sub.2 R.sub.1 R.sub.2)/(S.sup.2 +S/C.sub.2 R.sub.2 +1/C.sub.1 C.sub.2 R.sub.1 R.sub.2) (Equation 1) EQU H2=(S/C.sub.2 R.sub.2)/(S.sup.2 +S/C.sub.2 R.sub.2 +1/C.sub.1 C.sub.2 R.sub.1 R.sub.2) (Equation 2)
When the Q value of the TRAP and the BPF are represented as Q.sub.1 and Q.sub.2 respectively, those values are described by following Equation 3 and Equation 4 respectively. EQU Q.sub.1 =(C.sub.2 R.sub.2 /C.sub.1 R.sub.1).sup.1/2 (Equation 3) EQU Q.sub.2 =(C.sub.2 R.sub.2 /C.sub.1 R.sub.2).sup.1/2 (Equation 4)
Therefore, adjustment of the Q values in the TRAP and the BPF can be performed by controlling and adjusting at least one value selected from the group of C.sub.1, R.sub.1, C.sub.2, and R.sub.2.
The Q value can be enlarged by inserting an attenuator (ATT) to the inverting input of the second differential amplifier as shown in FIG. 9 and FIG. 10 as a method for providing a margin to the variable range of the Q value of the TRAP and the BPF. When an attenuation ratio of the attenuator (ATT) is represented as 1/.alpha., the transfer function H3 of the TRAP shown in FIG. 9 and the transfer function H4 of the BPF shown in FIG. 10 are described by Equation 5 and Equation 6 respectively. EQU H3=(S.sup.2 +1/C.sub.1 C.sub.2 R.sub.1 R.sub.2)/(S.sup.2 +S/.alpha.C.sub.2 R.sub.2 +1/C.sub.1 C.sub.2 R.sub.1 R.sub.2) (Equation 5) EQU H4=(S/C.sub.2 R.sub.2)/(S.sup.2 +S/.alpha.C.sub.2 R.sub.2 +1/C.sub.1 C.sub.2 R.sub.1 R.sub.2) (Equation 6)
Both the second term of the denominator of Equation 5 and Equation 6 are terms showing a Q value as a general style and both third terms are terms showing .omega..sub.0. Therefore, following Equation 7 and Equation 8 can be reached. Wherein, the Q value is described by Equation 8 which results from Equation 7. EQU .omega..sub.0 /Q=1/.alpha.C.sub.2 R.sub.2 (Equation 7) EQU .omega..sub.0.sup.2 =1/C.sub.1 C.sub.2 R.sub.1 R.sub.2 EQU Q=.alpha.(C.sub.2 R.sub.2 /C.sub.1 R.sub.1).sup.1/2 (Equation 8)
As understood from Equation 8, the Q value will be enlarged when .alpha. is enlarged (it means that the attenuation value is enlarged). Moreover, .alpha. is not an element of the square root operation. Therefore, a high Q value can be obtained more easily than the case when achieving a high Q value by adjusting the value of the capacitor or the value of the resistance.
Recently, many IC circuits employ and include various filters. Among those filters, in many cases, a steep characteristic will be required. In this case, a high Q value becomes indispensable. In order to enlarge the Q value in the above-mentioned equations Equation 3 and Equation 4, the value of R.sub.2 or C.sub.2 should be reduced, or the value of R.sub.1 or C.sub.1 should be enlarged. It is possible to achieve the Q value adjustment by changing the ratio of the resistance or the ratio of the capacitor if Q is about 2 to 3. However, there is a restriction on the upper limit of the Q value for practical use because there is a restriction on the value of the resistance and the value of the capacitors especially on the lower limit of those values for practical use without any problems.
Moreover, when adjusting the Q value automatically by regarding the type of the differential amplifiers included in the active filter as a variable conductance type, both values of the variable conductance elements of whole filter, which are corresponding to the variable conductance gm.sub.1 and gm.sub.2, should be adjusted as equivalent values in order to improve gm variable balance of whole filter. Therefore, the upper limit of the Q value which can be achieved will be further decreased because R.sub.1 and R.sub.2 can not be used for the adjustment of the Q value, and the adjustment of the Q value should be performed only by adjusting and controlling the value of the C.sub.1 and the C.sub.2. The Q value which can be achieved by the available capacitors will be about 3-4 at most considering the maximum value of the capacitors which can be used in practical use and the minimum value of the capacitors which can be used without problem on its accuracy.
In order to obtain a high Q value under such a condition, the circuit structure shown in FIG. 9 and FIG. 10 can be utilized. The Q value of the TRAP shown in FIG. 9 and the BPF shown in FIG. 10 can be adjusted by varying and adjusting the attenuation ratio 1/.alpha. of the ATT instead of varying the value of R.sub.1, R.sub.2, C.sub.1 or C.sub.2 as shown by FIG. 8. By this method, a very high Q value can be achieved.
However, there are the following problems. Most of analog integrated circuits of which the active filter is composed has a single power supply source. Most of those ICs are used with a single positive power supply voltage or a single negative power supply voltage to the earth potential of 0 V. A typical example circuit of the differential amplifier of the conductance part, which is included in the active filter shown in FIG. 7 to FIG. 10, is shown in FIG. 11. As understood from FIG. 11, when the circuit uses a single power supply source, the circuit elements are designed for performing around a working point supplied by the DC bias. As for the ATT used in the circuit shown in FIG. 9 and FIG. 10, a simple voltage dividing circuit, which can adjust the working point of the grounding type shown in FIG. 12 to 0 V, is not available. It is necessary to use the ATT which can perform around a working point by being supplied the DC bias as shown the circuit enclosed with broken line in FIG. 13. The emitter of the transistor Q.sub.1 corresponds to the input terminal of FIG. 12, and the emitter of the transistor Q.sub.2 corresponds to the grounding point of FIG. 12.
The buffer circuit including an op-amp shown in FIG. 14 (a) or the buffer circuit including transistor circuits shown in FIG. 14 (b) to (e) might be used instead of the transistor Q.sub.1 and transistor Q.sub.2 of FIG. 13. Moreover, when the Q value is a specific value, the ATT can be composed by utilizing a grounding type voltage dividing circuit as shown in FIG. 15. However, the adjustment of the DC bias of I/O becomes difficult. Therefore, the circuit elements for the DC adjustment will be necessary additionally. As mentioned above, the DC output level will be fluctuated if the Q value is varied. Therefore, varying and controlling the Q value becomes difficult, and the Q value will be limited to as a specific value. For this reason, the circuit configurations shown in FIGS. 14 (a) to (e) are hardly used, and the circuit configuration shown in FIG. 13 is mainly used.
In FIG. 13, in order to vary the Q value, the ratio of Ra and Rb are varied, and the amount of attenuation of the ATT is varied. Attenuation ratio 1/.alpha. for the output V.sub.ATT from the emitter of the transistor Q.sub.2 of the ATT part shown in FIG. 13 is described by Equation 9. EQU 1/.alpha.=Rb/(Ra+Rb) (Equation 9)
In order to enlarge .alpha. and to raise the Q value, it is necessary to enlarge the value of Ra and reduce the value of the Rb. However, the minimum value of the Rb is limited by the influence of the impedance re of the buffer (transistor) Q.sub.2 as the value of the Rb becomes small, and the maximum of the Q value is limited. For instance, if the current of the emitter of the transistor Q.sub.2 is assumed to be 100 .mu.A, the value of the re becomes 260 .OMEGA. and the value of the Rb becomes several k.OMEGA. or more when the influence of the re does not become a problem. It is necessary to reduce the value of the re of the Q.sub.2 in order to obtain a small value of the Rb, and it is necessary to increase the current of the emitter of the transistor Q.sub.2 in turn. However, this method is not preferable because the power consumption will be increase and the size of the transistor will become large which in turn increases the IC chip area.
If .alpha. is enlarged without reducing the value of the Rb, the value of the Ra becomes large. However, it is necessary to suppress the value of the Ra below hundreds of k.OMEGA. level in order to secure the accuracy of the value of the Ra. Moreover, if the ratio of the resistance Ra and the resistance Rb becomes too large, the relative accuracy of the Ra and the Rb worsens. In this case, it is necessary to suppress the difference between the Ra and the Rb within one digit order.
Considering the accuracy of the obtained attenuation ratio under above mentioned condition, it is preferable for setting the value of the Ra and the Rb within several k.OMEGA. and tens of k.OMEGA. respectively. For instance, the attenuation ratio 1/.alpha. becomes the value described by the Equation 10 when assuming re=260 .OMEGA., Rb=2 k.OMEGA., and Ra=50 k.OMEGA.. ##EQU1## In this case, the upper limitation of the obtained Q value becomes about 20. In Equation 10, because the a becomes 26 when re is 0 .OMEGA., it is understood that the .alpha. has decreased by about 10% by the influence of re. In order to reduce the influence of re, the obtained Q value should be lowered, the current of the emitter of the transistor should be increased or the absolute value of the Ra and the Rb should be increased. However, because the increasing of the current of the emitter as mentioned above leads to the increase of the power consumption and the IC chip area, in addition, the increasing of the absolute value of the Ra and the Rb leads to the increase of the IC chip area, the configuration shown by FIG. 13 is not preferable from the view point of the resource saving and the energy conservation. After all, about the value 20 becomes the upper bounds as for the Q value obtained by the simple conventional circuit configuration. On the other hand, a preferable value is 30 or more as the Q value for a filter having steep characteristics. Thus, the problem that the required filter characteristics cannot be achieved on the integrated circuit by a simple conventional circuit configuration is a general problem widely seen in all filter configurations such as the leap frog type filter and the bi-cut type filter wherein the value relation between two resistances affects the Q value.
There is a method for connecting plural stages of the ATT in serial as a simple method for the counter measure for the above mentioned problem. However, this method has the problem that the circuit scale becomes large, the accuracy decreases and the noise level increases as the number of stages increases. Moreover, the delay of the signal increases because the signal path of the feedback system becomes long. Therefore, there is a problem that a precise filter characteristic can not be obtained. Especially, the delay of the feedback system becomes a fatal problem in the active filter for high frequency use. For the same reasons, the leap frog type filter and the bi-cut type filter are not suitable for high frequency use.